cos[arcsin3/5-arccos(-5/13)]
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解决时间 2021-01-26 17:11
- 提问者网友:謫仙
- 2021-01-26 08:00
cos[arcsin3/5-arccos(-5/13)]
最佳答案
- 五星知识达人网友:酒醒三更
- 2021-01-26 08:27
cos[arcsin(3/5)-arccos(-5/13)]=?
解:arccos(-5/13)=π-arccos(5/13)
故原式=cos[arcsin(3/5)-π+arccos(5/13)]=cos[-π+arcsin(3/5)+arccos(5/13)]
=cos{-[π-arcsin(3/5)-arccos(5/13)]}=cos{π-[arcsin(3/5)+arccos(5/13)]}
=-cos[arcsin(3/5)+arccos(5/13)]
=-[cosarcsin(3/5)cosarccos(5/13)-sinarcsin(3/5)sinarccos(5/13)]
=-{[√(1-9/25)](5/13)-(3/5)√(1-25/169)]}
=-[(4/5)(5/13)-(3/5)(12/13)]=16/65
解:arccos(-5/13)=π-arccos(5/13)
故原式=cos[arcsin(3/5)-π+arccos(5/13)]=cos[-π+arcsin(3/5)+arccos(5/13)]
=cos{-[π-arcsin(3/5)-arccos(5/13)]}=cos{π-[arcsin(3/5)+arccos(5/13)]}
=-cos[arcsin(3/5)+arccos(5/13)]
=-[cosarcsin(3/5)cosarccos(5/13)-sinarcsin(3/5)sinarccos(5/13)]
=-{[√(1-9/25)](5/13)-(3/5)√(1-25/169)]}
=-[(4/5)(5/13)-(3/5)(12/13)]=16/65
全部回答
- 1楼网友:想偏头吻你
- 2021-01-26 09:22
-1
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